Difference between revisions of "1981 AHSME Problems/Problem 22"

(Created page with "==Problem== How many lines in a three dimensional rectangular coordiante system pass through four distinct points of the form <math>(i,j,k)</math>, where <math>i</math>, <math...")
 
m
(One intermediate revision by one other user not shown)
Line 1: Line 1:
 
==Problem==
 
==Problem==
How many lines in a three dimensional rectangular coordiante system pass through four distinct points of the form <math>(i,j,k)</math>, where <math>i</math>, <math>j</math>, and <math>k</math> are positive integers not exceeding four?
+
How many lines in a three dimensional rectangular coordinate system pass through four distinct points of the form <math>(i, j, k)</math>, where <math>i</math>, <math>j</math>, and <math>k</math> are positive integers not exceeding four?
  
$\textbf{(A)}\ 60\qquad\textbf{(B)}\ 64\qquad\textbf{(C)}\ 72\qquad\textbf{(D)}\ 76\qquad\textbf{(E)}\ 100
+
<math>\textbf{(A)}\ 60\qquad\textbf{(B)}\ 64\qquad\textbf{(C)}\ 72\qquad\textbf{(D)}\ 76\qquad\textbf{(E)}\ 100</math>
  
 
==Solution==
 
==Solution==
 
No solutions yet!
 
No solutions yet!

Revision as of 03:34, 14 June 2022

Problem

How many lines in a three dimensional rectangular coordinate system pass through four distinct points of the form $(i, j, k)$, where $i$, $j$, and $k$ are positive integers not exceeding four?

$\textbf{(A)}\ 60\qquad\textbf{(B)}\ 64\qquad\textbf{(C)}\ 72\qquad\textbf{(D)}\ 76\qquad\textbf{(E)}\ 100$

Solution

No solutions yet!